Coupling of light and matter can lead to the emergence of new collective phenomena, which render a separate description in terms of light or matter impossible. To understand and describe such cases, new composite light matter objects need to be introduced. In this chapter, we present theoretical studies of two examples of such systems. The first is an assembly of coupled Rabi cavities that shows coherent behaviour similar to Dicke super-radiance. The second is a Bose-Einstein condensate coupled to the optical modes of a cavity, that mediate an effective long range interaction between the atoms of the condensate and drive it into a supersolid phase.